The reason why I brought this idea out,is that it is suggested from time to time..and if it's placed at the right time in the history of the two nations..and if the variation in the POC is accurate..then I could fully see "America" being incorpertated into British North America. As for the name of this possible country,would it be possible for it to still be called "Canada" that is if the British eventually relinquish control of the land..
Your best bet is to have no ARW, in that sense, and tinker a bit with history to get whatever 'Canadian' traits you would like/feel are needed to replace 'American' ones.
After all, even today, taking politics out of things, both are still sea-to-sea English-speaking liberal nation states. Surely a loyalist continent-spanning British North America in general, assuming butterflies are fairly nonexistent, can also be one.